Erdős Problem 172
Is it true that in any finite colouring of there exist arbitrarily large finite such that all sums and products of distinct elements in are the same colour?
Mathematical statement
Is it true that in any finite colouring of there exist arbitrarily large finite such that all sums and products of distinct elements in are the same colour?
Statement source: Erdős Problems statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
erdos_172
theorem erdos_172 : answer(sorry) ↔ ∀ (n : ℕ) (color : ℕ → Fin n) (m), ∃ (A : Finset ℕ), A.card ≥ m ∧ ∃ c, ∀ (S : Finset A), S.Nonempty → color (∑ x ∈ S, x) = c ∧ color (∏ x ∈ S, x) = c := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References